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# solution_pdf5 - reddy(ar38357 – Vectors – clancy...

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Unformatted text preview: reddy (ar38357) – Vectors – clancy – (SCI411-2) 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points Consider two vectors vector A and vector B and their re- sultant vector A + vector B . The magnitudes of the vectors vector A and vector B are, respectively, 17 . 4 and 5 . 8 and they act at 83 ◦ to each other. vector A vector B vector A + vector B Find the magnitude of the resultant vector vector A + vector B . Correct answer: 19. Explanation: Let : a = 17 . 4 , b = 5 . 8 , and θ = 83 ◦ . b γ r a γ = 180 ◦ − 83 ◦ = 97 ◦ , so applying the law of cosines, r 2 = a 2 + b 2 − 2 a b cos γ = (17 . 4) 2 + (5 . 8) 2 − 2 (17 . 4) (5 . 8) cos 97 ◦ = 360 . 998 r = √ 360 . 998 = 19 . 002 (part 2 of 2) 10.0 points Find the angle between the direction of the resultant vector A + B and the direction of the vector A . Correct answer: 17 . 6372 ◦ . Explanation: a r β γ b Applying the law of sines, b sin β = r sin γ sin β = b sin γ r β = arcsin parenleftbigg b sin γ r parenrightbigg = arcsin parenleftbigg 5 . 8 sin 97 ◦ 19 parenrightbigg = 17 . 6372 ◦ . 003 10.0 points Consider the vectors vector A and vector B . vector A vector B Which sketch shows the vector vector A − vector B to the same scale?...
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